A232809 Decimal expansion of the surface index of a regular icosahedron.

5, 1, 4, 8, 3, 4, 8, 5, 5, 6, 1, 9, 9, 5, 1, 5, 6, 4, 6, 3, 3, 0, 8, 1, 2, 9, 4, 6, 1, 1, 6, 0, 1, 9, 0, 6, 4, 1, 0, 0, 8, 6, 4, 1, 1, 6, 3, 8, 6, 7, 2, 4, 1, 4, 8, 4, 5, 0, 7, 1, 3, 6, 7, 5, 3, 9, 8, 0, 3, 2, 4, 7, 9, 0, 5, 0, 8, 5, 7, 7, 1, 3, 0, 2, 9, 8, 3, 7, 3, 2, 5, 6, 2, 9, 9, 4, 3, 1, 0, 9, 6, 7, 4, 0, 0

Offset: 1

Author

Stanislav Sykora, Dec 01 2013

Keywords

• nonn
• cons
• easy

Comments

Equivalently, surface area of a regular icosahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: A232812 (tetrahedron), 6.0 (cube = hexahedron), A232811 (octahedron), A232810 (dodecahedron), and this one.

An algebraic integer of degree 12 with minimal polynomial x^12 - 41115600x^6 + 765275040000. - Charles R Greathouse IV, Apr 25 2016

Examples

			5.14834855619951564633081294611601906410086411638672414845...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..1000
• Wikipedia, Platonic solid.
• Index entries for algebraic numbers, degree 12

Crossrefs

Cf. A010527, A102208 (solid index of a sphere), A232808, A232810, A232811, A232812.

Programs

Mathematica

RealDigits[5*Sqrt[3]/(5*(3+Sqrt[5])/12)^(2/3), 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)

PARI

5*sqrt(3)/(5*(3+sqrt(5))/12)^(2/3) \\ Charles R Greathouse IV, Apr 25 2016

Formula

Equals 5*sqrt(3)/(5*(3+sqrt(5))/12)^(2/3).

Equals 10*A010527/A102208^(2/3).